Look at the bty argument in ?par, for example, bty="n". You can pass this argument in your call to plot.
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Glen_b♦May 24 '13 at 1:43

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FWIW, Tufte went further: he showed how in some cases erasing parts of the axes themselves provides additional information, effectively turning each axis into a visual display of the range of data. Inspired by this, in 1989 I wrote software to produce small multiple plots that incorporated this design (among many others inspired by Tufte and Bill Cleveland's group) and subsequently generated several million such graphics. When you have to mine so much data visually, such principles really work.
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whuber♦May 24 '13 at 13:42

@whuber Effectively, were you replacing the axes by a sort of rug plot?
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SilverfishFeb 24 at 17:08

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@Silver Drawing a rug plot is a separate issue--and I also did that, too. However, even in the absence of a rug plot you can choose where to stop and start drawing each axis. When you start it at the minimum and stop it at the maximum, you have achieved a visual representation of the full range of each marginal data distribution.
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whuber♦Feb 24 at 17:10

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@whuber Thanks, I now understand what you were referring to - Tufte calls this a "range-frame" (and suggests not only to stop the lines there at the extrema, but also to use the final labels to indicate their values - what he calls the "range-frame with range-labels"). For later readers wanting a reference, this is from Visual Display of Quantitative Information, Chapter 7 ("Multifunctioning Graphical Elements"). As this is a highly-viewed thread, it would be nice to see an illustration added (and given the question, some R code) of what "Tufte's axis" might really mean.
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SilverfishFeb 24 at 17:20